Towards a Universal Approach for the Analysis of Impedance Spectra of Perovskite Solar Cells: Equivalent Circuits and Empirical Analysis

Impedance spectroscopy is a powerful electrochemical small-perturbation technique that provides dynamic electrical data in solar cells. This technique has been widely used to characterize dye-sensitized solar cells and perovskite solar cells (PSCs). Physical parameters are normally obtained by fitting to an equivalent circuit, composed of electrical elements which theoretically correspond to physical processes involved in the photoconversion process. A variety of equivalent circuits to model the impedance spectra of PSCs are commonly used by different research groups. In this work, we evaluate their performance and adequacy. We demonstrate the analytical and numerical equivalence of impedance expressions for Voight, matryoshka, and hybrid circuits, which are used to fit a typical impedance spectrum of a PSC and compare the resulting parameters to the empirical values obtained without any equivalent circuit. The numerical equivalence can be demonstrated by using two- and three-component impedance spectra. In contrast, Maxwell-type equivalent circuits reveal parameters that have a more complex relation to empirical values. The presence of inductive effects such as "loops" and "negative tails" in impedance spectra are also discussed in terms of negative values of resistances and capacitances. We propose a general protocol to analyze impedance data of PSCs and to extract useful information from them.